I wish I knew what you meant by "list box". Do you mean a <select> element?
This made the most sense to me, in which case, those belong in forms and the form should submit, as they are want to do.
You can also have JS add "submit buttons" which, when clicked, use AJAX to ask the server to update that little section of the cart, and let users who have no JS just fill everything in at once and hit the real submit at the bottom. Those users would just get a whole page refresh like normal.
Could you be more descriptive?